Angle modulation includes both frequency modulation and phase modulation. Frequency modulation and phase modulation are related and can be converted from one to the other, as one skilled in the art understands.
Angle modulation (frequency and phase) produces multiple sideband pairs. These pairs are separated from the carrier in frequency by integer multiples of the modulating frequency. The power in the sidebands is derived from the carrier such that the total power is unchanged from no modulation to modulation. The amplitude of the carrier and each sideband pair is a function of the modulation index, and are determined by Bessel functions. A table and graph of Bessel functions are shown in FIG. 1.
The sideband structure of an angle modulated carrier is given in most electronic communication textbooks. The following characteristics of angle modulation are helpful in understanding the present disclosure. The amplitude of a carrier and sideband pairs are given by Bessel functions and vary with a given modulation index (the value of the modulation index indicates the power level of the carrier and sidebands). The total power of the modulated signal remains constant and the power in the sidebands is derived from the carrier. The vector sums of the odd order sideband pairs are in quadrature (+90, −90 degrees) with the carrier. These generate angle variation in the time domain. The vector sums of the even order sideband pairs are collinear (0, −180 degrees) with the carrier. These generate amplitude variations in the time domain.
A typical sideband can be represented by the following equation,sin(2πfct+M sin(2πfat))where:
fc=carrier frequency,
fa=audio frequency, and
M=modulation index.
What most texts fail to explain is that angle modulation is a nonlinear system. The graph of Bessel functions in most texts is given for a single sinusoidal modulating signal. When a complex modulating signal is used, “heat” frequencies are produced that are the sum and difference of the modulating frequencies. The vector sums of these “beat” frequency pairs are collinear with the carrier and produce amplitude variation in the time domain.
Space in the electromagnetic spectrum is at a premium. New services in voice and data are requiring more spectrum. Reducing the bandwidth required to transmit and receive information can open the available spectrum space for many more services.